Lambda Lambda-XiN Coupling Effects in Light Hypernuclei

Abstract

The significance of $\Lambda \Lambda$-$\Xi$N coupling in double-$\Lambda$ hypernuclei has been studied. The Pauli suppression effect due to this coupling in ${}_{\Lambda \Lambda }^6$He has been found to be 0.43 MeV for the coupling strength of the NSC97e potential. This indicates that the free-space $\Lambda \Lambda$ interaction is stronger by about $5^{\circ }$ phase shift than that deduced from the empirical data of ${}_{\Lambda \Lambda }^6$He without including the Pauli suppression effect. In ${}_{\Lambda \Lambda }^5$He and ${}_{\Lambda \Lambda }^5$H, an attractive term arising from $\Lambda \Lambda$-$\Xi$N conversion is enhanced by the formation of an alpha particle in intermediate $\Xi$ states. According to this enhancement, we have found that the $\Lambda \Lambda$ binding energy ($\Delta B_{\Lambda \Lambda }$) of ${}_{\Lambda \Lambda }^5$He is about 0.27 MeV larger than that of ${}_{\Lambda \Lambda }^6$He for the NSC97e coupling strength. This finding deviates from a general picture that the heavier is the core nucleus, the larger is $\Delta B_{\Lambda \Lambda }$.

16 pages with 2 figures

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